I was used to Ian Botham referring to me as his grandfather figure. Twenty years on, I have to face the fact of taking to dinner an actual grandson-generation figure, who is already at 22 captain of his country. It's a bit of a shock.

Graeme Smith wanted to meet me, too, partly because of his contact with my old Middlesex colleague Vintcent van der Bijl at Western Province cricket club. And in a way that's part of what is admirable about him: not that he wants to meet me, particularly, but his eagerness and willingness to learn, to meet players from earlier generations. I don't remember being open to such input when as a 22-year-old hopeful I was with the last England (pedantically, 'MCC') team to visit South Africa before the contentious but wholly correct refusal to 'play with apartheid'. I was so much less directed, single-minded, so much less clear in my aims, tasks and renunciations than the young fellow I picked up at his Nottingham hotel on the Friday of the last Test.

I was flighty, inwardly torn between sport and a more academic career, chronically unsure of myself, undeveloped as a batsman and a person. And here is this young man who has - as Len Hutton said of Frank Tyson and Brian Statham on their arrival in Perth for the 1954-55 tour of Australia - 'hardly played'. Yet he has scored three double centuries in his first 13 Tests, two in consecutive matches. Such was his apparent impregnability that it had taken a freakish dismissal earlier that same Friday evening - hit wicket to Andrew Flintoff for 35 - to get him out, an event that set in train an understandable temporary delirium in the England team. And apart from his batting, he had been selected to captain the side at a younger age than all but one of previous Test captains, of all the countries involved, going back to 1877.

What I found was an attractive mixture of youthfulness, even naivety, combined with the steely maturity and determination shown in his batting and in his approach to captaining a Test side. He has the male version of a young woman's charming blushes - expressions that at one and the same time betray both innocence and knowingness. In some ways, he's hardly more than a boy, envying the beach holidays of contemporaries on vacation from university, star-struck to be meeting not only grandfather figures but also the Michael Athertons of recent years, heroes of his while still in the third form (at the government-run boys' school, King Edward VII in Johannesburg), some of whom, of course, such as Shaun Pollock and Gary Kirsten, are in the team he's now captaining. He is very much the child of his background. 'There's such a variety of people here, and we are taken aback to hear Indians speaking with English accents, we're just not used to it. At home, if you're a Xhosa-speaker like Makhaya Ntini you speak English with a Xhosa accent; I myself speak Afrikaans with an English accent. We have a few laughs about it in the dressing room.' Here, in cosmopolitan England, everything seems a bit impure and confusing.

Combined with this inevitable ingenuousness there is, as I say, a strong centre. For example, he willingly makes renunciations in favour of his current role and career. Graeme, unlike his homophonically named father, Graham, who, having played at province level in all the junior sides up to under 19, gave up cricket to marry his athlete/tennis player wife (Graeme's mother), is determined to leave his love-life till after his cricketing education has moved on. Such will power! Having no girlfriend at the moment, he would like female company; but 'getting a girlfriend, or getting married, is down the list, way down the list just now'. He had a week off, but it took place in Ashton, near Canterbury, where 'there are lots of cathedrals and churches, but not much else to do'. And since he believes he should do all the things he expects of others, he did his full share of twelfth-man duties in Canterbury.

At some stage he also wants to do the university degree he declined to start at the usual age after leaving school. 'I admire Kirsten for doing one from 30-35.' (He thinks it's a BCom.) Smith foresees himself as 'ideally, retiring after 14 years as captain, with a bit of education behind me, and going into a good job. I can also imagine one day sitting at home in my slippers watching TV, with my family all around me and maybe a little bit of a stomach'. (No more caliper 'skin-fold' tests of the modern cricketer's training routine.)

But just now he has other things on his mind. Keen to learn, he is also well aware he has to pick and choose between what's worth learning, who's worth listening to. With characteristic good sense and thoroughness, he has someone whom he regularly goes back to for tips about his batting - technique and approach - if and when he needs it, the ex-South Africa opening batsman Jimmy Cook, who coached him when he arrived at Western Province at the age of 18. 'Jimmy is more detached than [the touring-team coach] Eric Simon, say, or [the team's batting adviser] Graeme Pollock,' both of whom talk to him and others about their approach to playing an innings.

'Simon was a bowling all-rounder as a player, but understands you as a batter, has a good brain and works on your level.' Smith spoke approvingly of Simon as being 'one step ahead', and pointed to his having spent a whole week in the nets with Jacques Rudolph and of the fact that they were still working on it after his two big scores against Kent.

Smith was quite clear about his priorities in life and at 18 made a considered choice to move from Johannesburg to Cape Town (in cricketing terms, from Gauteng/ Transvaal to Western Province). He wanted to see how tough it would be to find a place in the province team - and he wanted simplicity and honesty in contracts, which he didn't find with Gauteng's officials in Johannesburg. So he happily and confidently went south, to take his chances in a squad that already included Herschelle Gibbs, Jacques Kallis and Kirsten. This was, of course, also a decision to move from his family home to Cape Town, where he had to look after himself - a move that he reckons to have been 'one of my most important, making me pay my own bills and wash my own clothes'. This self-reliance has served him well in his subsequent cricket career. A few months before the move, and straight from school, in the English summer of 1999, Smith had spent two or three months at Hampshire, following in the footsteps of Barry Richards. Cook was county coach, so Smith stayed with him and played a few games for the second team. While here, he was a surprise selection for the South Africa A tour to the Caribbean, despite having played only three matches, all day-night games, for Gauteng. There he played against most of the West Indies Test players and performed well, playing in most of the major games, and averaging around 40. 'I grew up cricket-wise on this tour. It was a learning curve. I developed a hunger to play Test cricket.'

So Smith started with his new club already 'with a bit of a background. It wasn't as if I'd gone straight from schoolboy cricket into first-class cricket.' Though he played for the University of Cape Town team, he had no time for study. He had intended to ('probably computer studies; I would have liked to do psychology, like my younger brother who wants to be a forensic psychologist, but too much work for me'), but he was now a professional cricketer, playing top-level provincial cricket. He again averaged over 40 in first-class games that season, and scored 183 in the final of the four-day competition. Cricket offered glittering and exciting prospects. With a few more Board matches, he felt confident he'd play for South Africa quite soon. 'I always believed I'd make it at cricket, though I had, and have, no idea what else I might be or do.' His rise had already been meteoric, so it's understandable that now, three years later, 'it may be partly to do with these scores, but I don't think of myself as a "young" player', whose first-class career comprises only about 30 matches.

I said to him that at his age he seems to have an attitude to his cricket and the job that a lot of people struggle towards for the whole of their lives, some of them 'growing grey in the service of the game and learning nothing', as Ranjitsinhji put it. I tell him about my own arrogant failure to learn, from Wally Hammond, no less, when I was his age. Smith would have tried to listen, he said.

His parents married young, and had him, their first son, at 24. His father renounced 'childish things' in order to build up from scratch his own electrical engineering company, now specialising in reducing electricity bills for large companies. Mother gave up sport early and later shifted from her own career as a draughtswoman, designing and landscaping roads, to helping her husband in the business. Maybe there is some distant, way-back Scottish ancestry that makes the family so able to make serious-minded decisions. His parents must, I imagine, have had this ancestry in the back of their minds when they named their first son 'Graeme Craig'. I thought, possibly fancifully, that I could detect a Scottish type in his lean, wiry face. Seeing him interviewed on TV after the defeat at Trent Bridge, it occurred to me that he actually has something of the look of Steve Waugh, one of his heroes, with the shrewd, narrowed eyes and the ability to speak to the point without saying too much.

Smith asked me if we had curfews in my time. We didn't. 'That's the one rule that we have kept from the old regime, the 11.30 curfew during Tests. More so as not to open ourselves up to damaging press comment if things are going badly,' he said. They have given up the previous ruling of no alcohol for two days before a Test, despite his having 'had a few drinks a couple of days before one Test, which went badly, and after the match there were headlines in one paper about our drinking'. Wives and girlfriends are welcome for four weeks of the three-month tour. (When the couple at the next table asked for our autographs on leaving, Smith commented to me on the attractive girlfriend: 'You can see I don't get out much!') After the England tour, they have eight days at home, before setting off for seven weeks in Pakistan for more cricket and 'team carpet bowls in the evening'. He is glad he isn't English, post-Iraq and Afghanistan invasions. 'We'll wear our team gear all the time, not to be taken as British or American. It must be a nightmare for your guys playing in Pakistan after the war and all.'

Smith and Simon seem to get on well - in my experience an important ingredient of a successful tour. They make use of run-charts from the official scorers and also have a video analyst, who will collate for every player a personal video. He himself is not a hi-tech man, and struggles with laptops. But 'you can get from the video analyst whatever you ask for, every ball that pitches on your legs, or every short-pitched ball. It's very helpful.

' Before the Trent Bridge Test, he had had 10 days without an innings in the middle, so he spent an hour watching his big score at Lord's, 'to get the blood flowing, and rekindle good memories'. In the bus back from ground to hotel at close of play, the whole squad watch a video of personal highlights during the day's play. Smith thinks this works well, even with those who have had a bad day; they try always to find something good for everyone (though I imagine no video of that match could have done much for the confidence of Boeta Dippenaar, who scored nought and one).

Simon is one of the selectors and Smith's voice 'is heard'. He reckons they get what they want 'perhaps 95 per cent, no, 92 per cent of the time'. What astonished me was that the remaining selec tors weren't even in England at the time we spoke; they had just left, so now it would be necessary to consult by phone with them in South Africa before the team for the Headingley Test could be chosen. And the selectors, or even the chair (Omar Henry), can overrule from that great distance. He seemed remarkably sanguine about a system that, to me, is a recipe for disaster. On tour in my day, the team was selected by the manager, captain, assistant manager (if there was one) and two or three other players. The current South Africa party does have, however, as we did, a team management group; comprising manager, captain, assistant manager (Corrie van Zyl), physio and fitness trainer; plus Pollock, Boucher, McKenzie and Kallis. He agrees it's a big group, but it includes all the senior people who have an influence on the team, and it helps him to get everyone pulling together.

The match position when we met was that England had scored 445 (100 more, I thought, than they should have been allowed to get), and the pitch was clearly deteriorating. South Africa had struggled to 84 for two by close of play. Smith said: 'We had a better day today, after giving too many runs away yesterday. We kept England to two runs an over the whole day, and took seven wickets for 150 . . . the guys all believe we can get ahead.' I told him I thought England should win from this situation. I teased him that he'd most likely be batting again the next day, following on - an idea that seemed to him beyond the bounds of the possible.

Smith spoke about the England bowling. He has respect for James Anderson, though also certainly gratitude for his help in 'getting going' with a few loose balls with the new ball. 'If he gets it to swing he's brilliant, but if it doesn't swing too much, he'll give you a few bad balls. It's important for a batsman to have a bit of release now and then.' Andrew Flintoff had been the best, 'good pace, hits good areas consistently, hits the bat hard. He's in a similar position to Shaun [Pollock], who's bowled beautifully. Sometimes I cry for Shaun, he's beaten the bat so often and has so little to show for it.' This was, of course, before England batted a second time, when Pollock took six for 39.

When I doubted whether Ntini's skimmy action would be likely to cause as much havoc as the pinpoint accuracy of a Pollock, or the height and banging the ball into the pitch of a Flintoff or Steve Harmison, Smith demurred, suggesting that Ntini could bowl well on the present pitch. 'At Lord's he struggled up front with his length and line. But in his second spell onward he bowled really well. He's a great trier, keeps coming in. He finds the rises as he approaches the stumps hard to get used to, we don't have them in South Africa.' I explained that they are due to the age of the squares here and the constant relaying of pitches.

Another stance of Smith's that I admire is his attitude to the press. Perhaps he'll become more cynical, a more hardened old pro by the time he's the ripe age of 25. But during the Trent Bridge Test, when South Africa were having a less good time of it, he'd made a point of going to the press conference on every day. 'I've had a gut feel this is the right way to go. We've had two good matches and yesterday - was it only yesterday? It feels like the fourth day - was a tough day, the first one, so I felt I should go. I want the team to read in the papers what I have to say.' My own attitude used to be to go as little as possible and certainly not during the match. It seemed one burden too many. And I was well aware of the inevitably different agendas of player and journalist, the one group keen to be seen in the best possible light, the other interested either in the truth or in finding out sensational stories. I had a contempt for the latter motive and one element in me wanted to give such snoopers the minimum amount of information. I did have another aim, which was to speak as fully and frankly as I could to that part of the press that really wanted to know my version of what had gone on, without letting down the team, since I also thought I knew a lot about the match that they could not know. Now I can see more clearly that the reality of a complex event such as a cricket match can, at best, be approached from both perspectives, from the players' passionate involvement at close quarters and from the point of view of the more detached observation of the perceptive onlooker.

I asked him about how he finds the confidence to captain older and more experienced players. 'Shaun's been fine. He's got to get used to being a team member, and not captain. I don't have to say anything to him, he just gets on with it, he knows what to do. I think right now it's going really well between us. I communicate well with him, try to make him a part of the team. No, there aren't at the moment any problems with senior players. I sometimes have to come down hard on them, but they know it comes with the job. I have to stick my neck out sometimes. They know I don't have much time on my hands, that the pressure is on all the time. They have sympathy with whoever does the job. In fact, the senior guys see me as the right guy, they wanted me as captain. I don't think they think of me as only 22.

' I don't think he does, either. I reckon Smith already feels at home in Test cricket and pretty much at home in his new role. And though the youngest in the team until Monde Zondeki's selection, he can refer naturally to their 'young bowling attack', which means that 'I need to be in closer touch with them than I can be when I field in the slips'. He says he enjoys slip fielding 'I think I'm quite good there, I have big hands, anyway.'

He agrees with something I'd said about encouraging the whole team to think for themselves. Then he says: 'I think you've got to get the whole team believing in the way we're trying to go. Eric Simons tells me one thing that stands out in his mind. He was playing in one of his first games and Hansie [Cronje] came up and asked him what he thought we should do. He said that in the back of his mind he knew that Hansie's mind was made up, but it made him feel special that he asked him. That stuck in my mind, too. The manager reminds me that a lot of captains and senior players forget that the young guy or the guy that's new in the team sometimes has the best thing to offer.'

There's no open religion in the dressing room, nowadays. Unlike his recent predecessor, Cronje, Smith's view is: 'These things are individual. I believe in God in some way. But I'd feel awkward with team prayers.'

Smith sets high standards for himself and others. He wants to build a culture in which, when the team has a bad day, players look at themselves and acknowledge that they have to improve. 'It's just started happening during the last two months in South African cricket. I'm really beginning to get upset when people say, "It's just one of those things." That's not good enough. And I'm irritated with guys who won't listen; astonished to hear that some West Indies players don't rate Viv Richards.'

He admires, as I do, the transparent honesty in Atherton's book. 'I believe in honesty. There's no point in hiding things from the side or the people you deal with. You're not going to move forward as a side, or individually, like that.'

Smith also wants to develop a culture in which 'players think in terms of the purity of their task as representatives of their country'. He doesn't want people to play simply to make a good living and agrees with Steve Waugh's aim for Test cricketers. In Smith's words: 'UCB [the South African Board] think that because someone is developed enough to play at Test level, he's developed enough. I say let's develop him more, let's help the person grow as well as the cricketer. Take Makhaya [Ntini]. He's huge in South Africa, but also it would improve his money-earning capacity if he were to develop the one thing he lacks, thinking for himself and believing in himself as a thinker and cricketer. Let him take a management course, or whatever. If I get Makhaya to read a book on this trip I'll have done well.'

I can't argue with that. I can't argue with much that he says. One term I do have my doubts about is his image of the 'purity' of playing for one's country. Taken in one way I can see that he is saying something I totally agree with; that a selfish attitude is not conducive to a good team spirit, which involves everyone thinking for himself and contributing to the whole. He wants to work towards such an attitude. But I suspect there is something more lofty, more idealised, even more nationalistic in his conception of purity. Maybe deep down there is more than a trace of the Scottish Puritan in him, an image-source of cleansed selflessness.